Details

analyze455.0ms (5.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	74.9%	25.1%	5
0%	74.9%	25.1%	6
0%	74.9%	25.1%	7
6.2%	56.2%	37.6%	8
7.8%	53%	39.2%	9
10.9%	45.6%	43.4%	10
18.3%	31.4%	50.3%	11
19.1%	29.5%	51.3%	12
21.4%	24.8%	53.8%	13
25.8%	16.7%	57.5%	14

Compiler

Compiled 25 to 21 computations (16% saved)

sample33.0ms (0.4%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
3.0ms	37×	body	128	invalid
1.0ms	21×	body	128	nan

Compiler

Compiled 49 to 44 computations (10.2% saved)

simplify422.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (265.0ms)

Iter	Nodes	Cost
0	5077	36

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 6.0b

Counts

2 → 1

Compiler

Compiled 48 to 40 computations (16.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
0.1b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
5.5b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite51.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_12904` `*-un-lft-identity_binary64_12883`
20×	`add-cube-cbrt_binary64_12915`
18×	`log-prod_binary64_12966`
12×	`associate--l+_binary64_12822`
11×	`add-log-exp_binary64_12919`
9×	`distribute-rgt-in_binary64_12835` `distribute-lft-in_binary64_12834` `times-frac_binary64_12889`
8×	`add-exp-log_binary64_12918` `add-cbrt-cube_binary64_12916`
7×	`pow1_binary64_12941` `associate-+l+_binary64_12818`
5×	`associate-l_binary64_12826`
4×	`associate-r_binary64_12825`
3×	`associate-/r_binary64_12829` `associate-/l_binary64_12830`
2×	`associate-*l/_binary64_12828` `flip3-+_binary64_12886` `flip-+_binary64_12857` `sum-log_binary64_12971` `associate-/l/_binary64_12832` `sub-neg_binary64_12876` `diff-log_binary64_12972` `flip3--_binary64_12887` `flip--_binary64_12858`
1×	`log-pow_binary64_12969` `*-commutative_binary64_12816` `distribute-lft-out--_binary64_12837` `prod-exp_binary64_12929` `pow-prod-down_binary64_12951` `associate-+l-_binary64_12820` `distribute-lft-out_binary64_12836` `difference-of-squares_binary64_12852` `frac-2neg_binary64_12894` `div-exp_binary64_12931` `cbrt-unprod_binary64_12913` `clear-num_binary64_12882` `+-commutative_binary64_12815` `cbrt-undiv_binary64_12914` `unswap-sqr_binary64_12851` `div-inv_binary64_12880`

Counts

4 → 96

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
12.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
8.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

series961.0ms (11.1%)

Counts

4 → 12

Calls

4 calls:

324.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
302.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
187.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
148.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4926	2143
1	4926	2143

prune225.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 4.5b

Counts

109 → 10

Compiler

Compiled 3748 to 2555 computations (31.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z)
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.2b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) (-.f64 x 2069265617858471/2251799813685248))
5.5b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite52.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_12904`
22×	`*-un-lft-identity_binary64_12883`
20×	`add-cube-cbrt_binary64_12915`
12×	`log-prod_binary64_12966`
10×	`add-exp-log_binary64_12918` `add-cbrt-cube_binary64_12916`
9×	`pow1_binary64_12941` `add-log-exp_binary64_12919` `times-frac_binary64_12889`
8×	`associate-l_binary64_12826` `associate-*l/_binary64_12828`
7×	`associate-r_binary64_12825` `flip3--_binary64_12887` `flip--_binary64_12858`
6×	`associate--l+_binary64_12822` `distribute-rgt-in_binary64_12835` `distribute-lft-in_binary64_12834`
4×	`frac-sub_binary64_12892`
3×	`associate-/r_binary64_12829` `diff-log_binary64_12972` `associate-/l_binary64_12830`
2×	`*-commutative_binary64_12816` `prod-exp_binary64_12929` `associate-/l/_binary64_12832` `pow-prod-down_binary64_12951` `sub-neg_binary64_12876` `cbrt-unprod_binary64_12913` `unswap-sqr_binary64_12851`
1×	`log-pow_binary64_12969` `flip3-+_binary64_12886` `distribute-lft-out--_binary64_12837` `flip-+_binary64_12857` `associate--r-_binary64_12824` `difference-of-squares_binary64_12852` `frac-2neg_binary64_12894` `div-exp_binary64_12931` `clear-num_binary64_12882` `cbrt-undiv_binary64_12914` `associate--r+_binary64_12821` `div-inv_binary64_12880`

Counts

4 → 102

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
11.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) (-.f64 x 2069265617858471/2251799813685248))
10.0ms	(.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

series706.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

313.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) (-.f64 x 2069265617858471/2251799813685248))
189.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
146.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
58.0ms	(.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z)

simplify70.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4973	2398
1	4973	2398

prune195.0ms (2.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	114	10	124

Merged error: 4.5b

Counts

124 → 10

Compiler

Compiled 3982 to 2735 computations (31.3% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
5.5b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite27.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_12904` `*-un-lft-identity_binary64_12883` `add-cube-cbrt_binary64_12915`
9×	`cbrt-prod_binary64_12911` `times-frac_binary64_12889`
6×	`add-exp-log_binary64_12918` `add-cbrt-cube_binary64_12916`
4×	`pow1_binary64_12941` `add-log-exp_binary64_12919`
3×	`associate-/r_binary64_12829` `associate-/l_binary64_12830` `pow1/3_binary64_12962`
2×	`associate-/l/_binary64_12832`
1×	`flip3-+_binary64_12886` `flip-+_binary64_12857` `frac-2neg_binary64_12894` `div-exp_binary64_12931` `clear-num_binary64_12882` `cbrt-undiv_binary64_12914` `div-inv_binary64_12880`

Counts

4 → 62

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
4.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series599.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt.f64 x)
154.0ms	(cbrt.f64 x)
146.0ms	(cbrt.f64 x)
142.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify70.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4689	1143
1	4689	1143

prune148.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	75	9	84

Merged error: 4.5b

Counts

84 → 9

Compiler

Compiled 3389 to 2074 computations (38.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.2b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.3b	(/.f64 1 (/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936)))
5.5b	(/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936))

rewrite71.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64_12889`
66×	`add-sqr-sqrt_binary64_12904` `*-un-lft-identity_binary64_12883`
62×	`add-cube-cbrt_binary64_12915`
19×	`add-exp-log_binary64_12918`
18×	`associate-/r*_binary64_12829`
13×	`add-cbrt-cube_binary64_12916`
12×	`log-prod_binary64_12966`
11×	`associate-/r/_binary64_12831`
9×	`add-log-exp_binary64_12919`
8×	`pow1_binary64_12941` `div-exp_binary64_12931`
7×	`associate-+l+_binary64_12818`
6×	`flip3-+_binary64_12886` `associate--l+_binary64_12822` `distribute-rgt-in_binary64_12835` `flip-+_binary64_12857` `associate-/l*_binary64_12830` `distribute-lft-in_binary64_12834` `div-inv_binary64_12880`
5×	`associate-l_binary64_12826`
4×	`associate-r_binary64_12825` `cbrt-undiv_binary64_12914`
2×	`associate-*l/_binary64_12828` `sum-log_binary64_12971` `1-exp_binary64_12924` `frac-2neg_binary64_12894` `clear-num_binary64_12882` `rec-exp_binary64_12930`
1×	`log-pow_binary64_12969` `*-commutative_binary64_12816` `distribute-lft-out--_binary64_12837` `prod-exp_binary64_12929` `pow-prod-down_binary64_12951` `associate-+l-_binary64_12820` `sub-neg_binary64_12876` `distribute-lft-out_binary64_12836` `difference-of-squares_binary64_12852` `diff-log_binary64_12972` `cbrt-unprod_binary64_12913` `pow-flip_binary64_12954` `flip3--_binary64_12887` `+-commutative_binary64_12815` `unswap-sqr_binary64_12851` `inv-pow_binary64_12965` `flip--_binary64_12858`

Counts

4 → 163

Calls

4 calls:

19.0ms	(/.f64 1 (/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936)))
13.0ms	(/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936))
12.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

series900.0ms (10.4%)

Counts

4 → 12

Calls

4 calls:

311.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
243.0ms	(/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936))
194.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
152.0ms	(/.f64 1 (/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936)))

simplify97.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5664	4956

prune382.0ms (4.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	174	10	184

Merged error: 3.8b

Counts

184 → 10

Compiler

Compiled 6415 to 4458 computations (30.5% saved)

regimes847.0ms (9.8%)

Compiler: Compiled 10821 to 8647 computations (20.1% saved)

bsearch33.0ms (0.4%)

Steps

Iters	Range		Point
7	3.5573234579364264e+24	1.2182296540611373e+26	5.255504350346211e+25

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	108	101
1	108	101

end0.0ms (0%)

sample2.1s (24.8%)

Algorithm

1×

intervals

Results

579.0ms	8000×	body	128	valid
88.0ms	1215×	body	128	invalid
48.0ms	747×	body	128	nan

Compiler

Compiled 1466 to 1165 computations (20.5% saved)

Details

analyze455.0ms (5.3%)

sample33.0ms (0.4%)

simplify422.0ms (4.9%)

prune7.0ms (0.1%)

localize17.0ms (0.2%)

rewrite51.0ms (0.6%)

series961.0ms (11.1%)

simplify90.0ms (1%)

prune225.0ms (2.6%)

localize17.0ms (0.2%)

rewrite52.0ms (0.6%)

series706.0ms (8.1%)

simplify70.0ms (0.8%)

prune195.0ms (2.3%)

localize24.0ms (0.3%)

rewrite27.0ms (0.3%)

series599.0ms (6.9%)

simplify70.0ms (0.8%)

prune148.0ms (1.7%)

localize18.0ms (0.2%)

rewrite71.0ms (0.8%)

series900.0ms (10.4%)

simplify97.0ms (1.1%)

prune382.0ms (4.4%)

regimes847.0ms (9.8%)

bsearch33.0ms (0.4%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.1s (24.8%)

Profiling